Abstract: An increased mortgage cap was introduced in 2010, and as of May 1st 2016 an amortization requirement was introduced in an attempt to slow down house price development in Sweden. Fluctuations in the house prices can significantly influence macroeconomic stability, and with house prices in Stockholm rising even more rapidly than Sweden as a whole makes the understanding of Stockholm’s dynamics very im- portant, especially for policy implications. Stockholm house prices between the first quarter of 1996 and the fourth quarter of 2015 is therefore investigated using a Vector Error Correction framework. This approach allows a separation between the long run equilibrium price and short run dynamics. Decreases in the real mortgage rate and in- creased real financial wealth seem to be most important in explaining rising house pric- es. Increased real construction costs and increased real disposable income also seem to have an effect. The estimated models suggest that around 40-50 percent, on average, of a short-term deviation from the long-run equilibrium price is closed within a year. As of the last quarter 2015, real house prices are significantly higher compared to the long run equilibrium price modeled. The deviation is found to be around 6-7 percent.
Keywords: House prices, Vector error correction, Error correction, co-integration, overvaluation, long run equilibrium.
What is driving house prices in Stockholm?
Josefin Ångman*
Master thesis (EC9901) Department of Economics
Spring term 2016
1. Introduction
It is not an understatement to say that the rising house prices in Sweden have been widely discussed over the last years. An increased mortgage cap1 was introduced in 2010, and as of May 1st 2016 an amortization requirement2 was introduced in an at- tempt to slow down price development. Sweden also has had historically low repo rates, at the time of writing -0.5 percent. As stated by the Director General Erik Thedéen of the Financial Supervisory Authority; “The amortization requirement is needed to re- duce the risks connected with household debts and it might also contribute to a slow- down in the increase of home prices.” (FSA, 2015a). It is not surprising that the rapid increase of real house prices has lead to debate and regulation. Fluctuations in the hous- ing market can significantly influence macroeconomic stability. The main reason is that housing is probably the main asset and source of debt making it the largest liability among the majority of households in many countries. This means that falling house prices have serious consequences for macroeconomic stability. Examples of conse- quences from falling property prices on the macro economy are the Japanese property crisis in the 90s, and the more recent Irish and Spanish property crisis and the subprime crisis in the US in 2008. Therefore, it is highly motivated to further investigate the dy- namics of house prices since it is very relevant for policy implications.
Can house price development be described through a long run equilibrium relationship or does it exist other factors driving house prices that are not explained by fundamen- tals? This also leads to the question on whether house prices are in line with those fun- damentals. Compared to the rest of Sweden, house prices in Stockholm have risen faster than the rest of the country as a whole. Stockholm is the largest city in Sweden and also the capital, making it an interesting geographical area to study. Thus, the purpose of this thesis can be summarized by the following questions:
What are the dynamics of Stockholm house prices? Can the development of house pric- es in Stockholm be described through a long-run relationship and what does it look like? If such long run relationship exists, are prices in line with those or does it exist overvaluation?
1 The Mortgage cap was increased from 10 to 15 percent.
2 The amortization requirement applies to new mortgages exceeding 50 percent of the residential value. New mortgages exceeding 70 percent of the property value will be amortized by at least 2 percent of the toatale mortgage per year, and at least 1 percent when the loan amounts to between 50 and 70 percent of the property value (Sveriges Riksadag, 2016).
The questions are answered using Vector Error Correction models (VECM), where the long run and short run dynamics of the house prices are investigated using data between the first quarter of 1996 and the last quarter of 2015. Forecast error variance decomposi- tions are computed to examine how and what shocks cause movements in house prices.
Impulse response functions are used to show the magnitude and duration of the effects from a specific structural shock. For robustness there is also an Error Correction Model (ECM) estimated.
The study’s contribution is threefold. First, no existing literature on the dynamics of Swedish house prices have focused specifically on Stockholm. Secondly, the method used in previous studies is strictly biased towards the single equation error correction framework. Applying a bivariate vector error correction framework, allowing a more diversified analysis, is therefore a real contribution to existing literature. Finally, it pro- vides further insight on the dynamics of house prices.
An existing long run relationship between house prices and its fundamentals is found.
Real financial wealth and the mortgage rate seem most influential on house prices. Real construction cost also influence house price movements. Real disposable income does not seem to influence Stockholm house prices to the same extent found in previous studies on the Swedish market. The main reason could be that financial assets are more important in Stockholm since house prices are higher and the capital requirement there- fore gets larger in an absolute sense. Deviation from the long-run equilibrium level is found to be closed by 40-50 percent within a year. However, comparing house prices to long run equilibrium modelled, Stockholm house prices are overvalued with 6-7 percent as of the last quarter 2015. The deviation from the long run equilibrium modelled is statistically significant on the 5 percent level.
The reminder of this thesis is organized as follows; the following section gives an intro- duction to the theoretical background of house price dynamics, where the economic theory, the long run equilibrium house price modeling will be built on, is described. In section three previous studies on the subject are discussed. In the fourth section the econometric model is specified. Section five contain a description of the data. The esti- mations and methods applied are presented, analyzed and discussed in relation to the
questions raised in this thesis and compared with existing studies in section six. In sec- tion seven there will be a brief summary in the form of a conclusion.
2. Theoretical Background
Traditionally the Stock-Flow approach has been used in macroeconomic modeling of durable goods such as the house price (Meen, 2012 p. 67; Caldera Sánchez, A. & Jo- hansson; DiPasquale & Wheaton, 1994; amongst others). A stock-flow model allows for a distinction between the housing stock, which is quite rigid in the short run, and the flow of residential investment, reacting rapidly to changes in macroeconomic condi- tions. Because of this property the model is a good fit for the needs of this study. Fur- thermore, it is a good foundation for the type of econometric modeling used3.
There is no absolute consensus on the exact variables and how they should be measured in the Stock-Flow setting. Therefore, a general description of the model is made, fol- lowed by a deeper motivation of the variables chosen to be included in this specific study.
The demand of housing, 𝐻., can simply be stated by the following equation:
𝐻. = 𝑓 𝑃, 𝑈, 𝐷 , (1)
where 𝑃 is the real house price level, 𝑈 is the expected real cost of owning a dwelling and 𝐷 accounts for other fundamental variables affecting housing demand.
The supply of housing, 𝐻5, can be defined as:
𝐻5 = 𝑓 𝑃, 𝑆 . (2)
Where 𝑆 stands for other fundamental variables affecting the demand for housing. In equilibrium housing demand equals housing supply and the reduced form equation for the price level of housing is:
𝑃 = 𝑓(𝐷, 𝑆, 𝑈). (3)
It is necessary to define the expected real user cost of house ownership, U, in more de- tail. The most important factor of real user costs is the real mortgage rate defined as the inflation adjusted mortgage rate after tax-deductibility (Claussen 2013, DiPasquale &
3 The econometric model is described and discussed in section four.
Wheaton, 1994; Loenhard et al, 2008; Oikarinen, 2005, amongst others). The real mort- gage rate (𝑅) can formally be describes as:
𝑅; = 𝑟; 1 − 𝜏; − 𝜋;. (4)
Where 𝑟; is the real mortgage rate, 𝜏; is the share of tax deductible mortgage rate and 𝜋; denotes inflation. Lowering of the real mortgage rate decrease user costs. This means that the higher the tax deductibility is and the higher inflation, the lower will user costs be (holding the mortgage rate constant). Other factors important for user cost are for example real estate taxes, expectations about future house prices, risk premiums, depre- ciation, capital tied in housing and inflation expectations (Loenhard et al, 2008; Oi- karinen, 2005).
Another variable affecting house prices and demand for houses, frequently used in the stock flow modeling of house prices, is the rental price level (DiPasquale & Wheaton, 1994). The rental price is the alternative cost of owning a dwelling since it is the cost one would face not owning a dwelling. Therefore, increased rental prices would mean increased demand for owning a dwelling. However, it would probably not be appropri- ate to include this variable in the Swedish case since, as Boverket (2014) mentions, in- ternationally Sweden has a unique and complex rent control system. Therefore, it would probably not work very well including it in the model for the Swedish case (Claussen, 2013).
Other variables that could affect housing demand are demographics, financial wealth, and income (Oikarinen, 2005; Leonhard et al, 2013; amongst others). Increased popula- tion holding housing supply constant puts upward pressure on housing. The age distri- bution of the population could also have an effect (DiPasquale & Wheaton, 1994). In- creased income and financial wealth mean increased demand for housing creating de- mand of more, larger and more expensive housing. Also, credit availability could influ- ence demand. Including it in the model would be reasonable if there is credit rationing or other frictions in the credit markets (Claussen, 2013). Therefore, such a variable will not be included since the study is preformed during the period after the credit liberaliza- tion in Sweden.
The most important variable affecting housing supply is construction costs and would naturally affect house prices. The higher the construction costs, the lower will the level of new dwellings be and thereby future supply is reduced. Lower supply will have an increasing effect on house prices. Therefore, it is likely that there is an endogeneity problem present since higher prices would in turn make more construction projects profitable (DiPasquale & Wheaton 1994; Oikarinen, 2005). This means that the will- ingness to supply housing would increase and the growing demand for construction workers and materials would raise construction costs.
3. Previous Studies
Since the theory behind house price development now has been clarified, it is appropri- ate to continue with the finding of empirical studies on the subject. Since the geograph- ical area of this study is Stockholm it is appropriate to look at the studies most relevant for this market. Unfortunately, there are no previous studies to my knowledge purely on the Stockholm market. Therefore, the next best thing is to look at studies regarding Sweden. There is also a study on Helsinki mentioned since it relates in the way that it was conducted on a metropolitan area within the Nordic region.
The first study to be brought up was conducted by Hort (1998). In this study, panel data of 20 urban areas in Sweden from 1967 to 1994 was used estimating an error-correction model of real house price changes using the Engle Granger two step method. The ex- planatory variables used were real construction costs, pre tax real income, interest sub- sidies, the net lending ratio4, the population aged between 25-44 years as well as a trend parameter which the author argues is ”a proxy for some factors which are not adequate- ly accounted for in the model” (Hort, 1988, pp 106). Hort finds that fundamentals such as income, user costs, and construction costs significantly impacts development of real house prices.
Using annual data between January 1971 and February 1997 Barot (2001) applied an ECM framework estimating a demand and supply model for Swedish house prices.
Here, short run demand dynamics were estimated using the real after-tax long interest rate, financial wealth, the employment rate, rents and population. Long run demand was
4 The ratio of net lending to disposable income for the household sector (Hort, 1998).
modeled using debt to income, debt to financial wealth, private housing stock to in- come, the stock of rental housing to private housing stock, and the real after- tax long interest rate. The long and short run supply side was based on the Tobin’s q-index in the form of a ratio of current housing price to current construction costs, the short interest rate and stock market returns. The main findings were that the development in house prices during the period as well as short run adjustments could be well explained by demand and supply fundamentals.
Barot & Yang (2002) applied a similar method as Barot (2001) on quarterly data be- tween the first quarter 1970 and the forth quarter 1998 to estimate housing demand and investment supply models for Sweden and the UK. Their conclusion was that Sweden had a semi-elasticity to interest rates of 2.1. The speed of adjustment following higher demand and supply was from the demand-side 12 percent and supply side 6 percent.
In a panel study on 15 OECD countries, including Sweden, Adams and Füss (2010) used quarterly data between 1975 and 2007 and applied an ECM framework. The long run dynamics were modeled in the same way for all countries using dynamic ordinary least squares (DOLS) while the short run dynamics were assessed country by country.
The fundamental factors found to have a positive effect on house prices were an indica- tor of economic activity generated by real money supply, real consumption, real indus- trial production, real GDP and employment. Also the short-term interest rate and con- struction cost had a positive effect and negative effects stemming from an increase in the long-term interest rate.
Using annual panel data estimations on all Swedish counties Leonhard et al (2013) in- vestigated if the house prices were driven by housing shortage. They argue that the main explanation of rising house prices are rising income, low interest rates and backward looking expectations or speculation. They also claim that house prices are driven to a larger extent by increased income than overcrowding even though demographics, such as increasing population in relation to new dwelling has had a significant effect.
Caldera Sánchez & Johansson (2011) also applied an ECM framework on a quarterly panel of 21 OECD countries including Sweden between 1975 and 2008. The explanato- ry variables used to model the long and short run dynamics in this study were real in-
come, real interest rate, dwelling stock, population between 25-44 years and construc- tion costs. Their estimates suggest that the responsiveness of housing supply to price changes varies substantially across countries. New housing supply was found to be rela- tively more flexible in some of the Nordic countries compared to other European coun- tries. Also, the responsiveness of housing supply did, alongside with geographic and urban characteristics, depend on policy regarding land use and planning regulations.
In a more recent study Claussen (2013) used the two step Engle Granger procedure to estimate an ECM investigating whether the Swedish housing market was overvalued or not. The sample consisted of quarterly observations between 1986 to the second quarter 2011. Using real house prices measuring house price development the main findings was that rising household income and falling mortgage rates were the main reason be- hind increases in Swedish house prices. The explanatory variables used were the after tax mortgage rate5, real disposable income and real financial wealth. There was also an attempt to include construction costs, but they did not work well in the model. Accord- ing to this study Swedish house prices did not seem to be overvalued at the time.
The most recent study on house price dynamics on Swedish data is a paper by Turk (2015). Quarterly data from the first quarter 1980 to the second quarter 2015 was used to estimate ECMs investigating the interaction between household debt and house prices in Sweden. According to Turk’s estimates, Swedish house prices were around 5 percent above the long-run level at the second quarter of 2015. Since the interest rates are cur- rently relatively low by historical standards it is argued that a full reversion to its mean of 1.5 percent since 2000 would lower the equilibrium price level of houses with 6 per- cent, implicating an overvaluation of the housing market of 12 percent. Turk also argues that a price deceleration in the future is more likely than a decline. In the long run, the demand side is represented by real household disposable income per capita, the real after tax mortgage rate, real household financial assets, net liabilities per capita and net migration inflow per capita.
5The real mortgage rate was calculated using a weighted average of a 3-month treasury bill, 2-year and a 5-year government bond.
The weights were the historical share of household mortgages on respective floating, fixed up to 5 years, and fixed more than 5 years interest rates (Claussen, 2013).
In a study on the Helsinki housing market Oikarinen (2005) use quarterly data between the first quarter of 1975 and the second quarter 2005 to investigate the long-run rela- tionship between a number of fundamental factors and house prices. The price level of the Helsinki housing market was found to be in line with fundamentals at the time. The main explanation for the substantial increase in house prices during the 10 most recent years of the study was found to be rapid growth in real disposable income and a decline in the mortgage rate. Real house prices were found to be primarily driven by demand factors, even in the long run. About 10-15 percent of the deviation between the long run price level and actual price level was found to vanish during a quarter.
Summing up, previous studies have found that house price development can be well explained by fundamental factors. Even though the studies do not include exactly the same variables, the most important ones seem to be real income, the real mortgage rate, financial wealth, construction costs and some variable accounting for demographics.
Almost all previous studies have used the ECM approach. In the next section this ap- proach as well as the VECM will be discussed.
4. Empirical Model
In the short run it is possible that house prices deviate from their fundamental value.
Empirical evidence on this starts with Case and Shiller (1989), indicating that it could take time for the housing market to adjust towards its equilibrium level. The most obvi- ous reason for this is that although housing demand might be flexible in the short run, the supply of housing is rather inflexible in the short time horizon. Following this ar- gument, the empirical model most suitable is the bivariate Vector error correction mod- el (VECM) or the single equation Error correction model (ECM) allowing the modeling of the relationship discussed earlier, with both long and short-run dynamics.
Estimating a VECM or ECM requires the variables in the model to be non-stationary in levels. If there exists a stationary linear combination of the non-stationary variables, the variables combined are said to be co-integrated and the models can be estimated. This means that the 𝛽B, 𝛽C… 𝛽E forms a co-integrating vector. (Wooldrich, 2010).
Describing the more complex VECM first, following the definition of co-integration of Campbell and Perron (1991), A 𝑛𝑥1 vector of the variables 𝒚; is said to be co- integrated if there exists at least one nonzero n-element vector 𝛽I such that 𝛽′I𝑦; is trend stationary, where 𝛽I is referred to as a co-integrated vector. It is such that 𝒚; is cointe- grated of the rank 𝑟 if 𝑟 linearly independent vectors 𝛽I exixts.
Following Pfaff (2005), a vector autoregressive model (VAR) of order 𝑝 will be esti- mated:
𝒚; = 𝜫B𝑦;NB+. . . +𝜫P𝑦;NQ+ 𝝁 + 𝜱𝑫;+ 𝜀; for 𝑡 = 1, … , 𝑇, (7)
where the vector 𝒚; contains the elements of house prices (ℎ𝑝𝑖), income (𝑖), mortgage rate (𝑟), financial wealth (𝑓), construction cost (𝑐𝑐) and the variable capturing the de- mand pressure (𝑑𝑒𝑚). In the model 𝑫; represents seasonal dummy variables and the vector 𝝁 is a vector of constants. The (kx1) error term 𝜀; should be i.i.d as 𝜀; ~𝑁(0, ∑).
From the above equation one can derive the following VECM:
∆𝒚;= 𝚪B∆𝑦;NB+. . . +𝚪QNB∆𝑦;NQdB+ 𝜫𝑦;NQ+ 𝝁 + 𝜱𝑫;+ 𝜀;, (8) 𝚪I = − 𝑰 − 𝜫B− … − 𝜫I , for 𝑖 = 1, … , 𝑝 − 1, (9)
𝜫I = − 𝑰 − 𝜫I−. . . −𝜫I , (10)
where 𝑰 represents the (𝑲 𝑥 𝑲) identity matrix. The 𝚪I matrices contains the cumulative long-run impacts. Since the variables in the system are stationary of order one, this means that the left hand side of the VECM is stationary. Therefore, the term 𝜫𝑦;NQ must also be stationary in order for the VECM to balance. There are three conditions to fulfill this property:
𝑖) 𝑟𝑘 𝜫 = 𝐾, 𝑖𝑖) 𝑟𝑘 𝜫 = 0, 𝑖𝑖𝑖) 𝑟𝑘 𝜫 = 𝑟 < 𝐾,
𝑟 𝑥 𝑘 determines the rank of the matrix. In i, the VECM represents a standard VAR- model in levels. In the second case, when 𝛱 = 0, there exists no linear combination making 𝛱𝑦; stationary. This means that the VECM represents a VAR-model in first differences. The occurrence of the third alternative means that the matrix does not have
full rank. In this case there exist two 𝐾 𝑥 𝑟 matrixes, 𝛼 and 𝛽, such that 𝛱 = 𝛼𝛽´, mean- ing that 𝛼𝛽´𝑦;NQ is stationary and thus, the matrix vector product 𝛽´𝑦;NQ is stationary.
Hence, the r linear independent collumns of 𝛽 represents the co-integrated vectors and the rank of 𝛱 equals the co-integrating rank of 𝑦;. The parameters in 𝛼 and 𝛽are unde- fined due to the fact that any non-singular matrix 𝛯 would generate 𝛼𝛯(𝛽𝛯NB)´. Thus, the only co-integrating space spanned by 𝛽, will be determined. The solution is that one element of 𝛽 is normalized to one. The speed of adjustment to the long-run equilibrium level is determined by the s elements of the speed of adjustment matrix 𝛼.
A co-integrated relationship can also be described using a one equation ECM. This method is applied in most previous studies (see for example Claussen, 2013; Caldera Sánchez & Johansson, 2011; Hort, 1998; Oikarinen, 2005). Here house prices are mod- eled in the follow way:
𝑝;∗ = 𝛽p+ 𝛽B𝑥B+ ⋯ + 𝜀. (11)
The equilibrium price level (𝑝;∗) is described as a linear function of a set of 𝑛 explana- tory variables where 𝛽B, 𝛽C… 𝛽E are parameters to be estimated and 𝑥B, 𝑥C… 𝑥E are the values for the n explanatory variables at time 𝑡.
Denoting the house price in period 𝑡 as 𝑝;and ∆ be the one period difference operator such that ∆𝑝; = 𝑝;− 𝑝;NB and thus ∆𝑝;NB = 𝑝;NB− 𝑝;NC and so on the short run dy- namics in the ECM can be described as:
∆𝑝; = 𝑐 + 𝛼 𝑝;NB− 𝑝;NB∗ + tsvBu 𝛿s∆𝑝;N𝑧+ tsvpu 𝛾B,s∆𝑥B,;Ns+ tsvpu 𝛾E,s∆𝑥E,;Ns+ 𝜀;,
(12)
where 𝑐, 𝛼, 𝛿5 and 𝛾5 are parameters to be estimated and 𝜀; is an iid error. The number of lags of the difference to include will be left open until the estimations. The short run adjustment parameter is represented by 𝛼 and states how much of the difference be- tween the current price level and the equilibrium price level is corrected for in each pe- riod. The expected sign is negative between zero and minus one. The value of 𝑝;NB∗ in equation 12 is given by equation 11. Equation 12 is the error-correction model to be estimated.
However, it is important to acknowledge that the number of parameters to be estimated both in the VECM and ECM increase with the number of lags in the model and the
available length of the time series restricts the number of available observations. This means that one should choose an as parsimonious model as possible6.
The names of the models are intuitive since it has a built in mechanism to gradually correct the difference between the current price and the long run equilibrium price i.e.
the “error”. When 𝑝;NB is larger that 𝑝;NB∗ , that is above the equilibrium price level, the error correction term 𝛼, which is negative adjust the price downwards towards its equi- librium level. Naturally, if the price level is above equilibrium the error corrects it downwards.
The choice between the ECM and VECM is important since the ECM requires all vari- ables to be weakly exogenous towards house prices (Chen, 2006). The most obvious example contradicting the weak exogeniety requirement is that increases in the supply of new dwelling should theoretically increase supply and thereby have a decreasing effect on house prices. At the same time, it is also the case that increasing supply lead- ing to lower house prices will have a decreasing effect of the willingness to supply new dwellings. Thus it is safer to treat all variables in the system as endogenous; otherwise, the estimation could suffer from potential simultaneity biases. Another advantage with the Johansen procedure is that it estimates both the long run equilibrium and short run dynamics at once while the Engle-Granger does this in two steps. Furthermore, the Jo- hansen procedure can, in contrast to the Engle-Granger method, estimate the number of co-integrating vectors and not only if there exists a co-integrating vector or not. With 𝑛 variables there can be at a maximum 𝑛 − 1 co-integrating relationships. This means that if there exists more than one co-integrating vector the two-step procedure is directly inappropriate (Enders, 2010). However, the Johansen method relies on asymptotic prop- erties and could therefore be sensitive to specification errors in limited samples7.
It appears like the VECM is more suitable than the ECM, even though previous studies have used the ECM. Therefore, the VECM will be the main approach and the ECM framework will be used for robustness.
6 Wooldridge (2010) argues that there are no hard rules to follow when it comes to lag length but it is often dictated by the frequen- cy of the data as well as sample size.
7 More technical information on the Johansen procedure can be found in Johansen & Juselius, 1990.
5. Data
The data is measured quarterly. Some data is collected on monthly or even daily fre- quency is transformed to quarterly taking a weighted average. The sample contain no observations prior to 1996 since there were no data available before that date on some variables. A lot of structural changes in the financial sector and credit markets also hap- pened before this time. Not including observations prior to this period means that the structural break in the credit market from the credit de-regulation is avoided8 (Claussen, 2013). There might still be a risk that there are breaks in the series since there were an increase in the collateral requirement from 10 percent to 15 percent as of October 1st 2010.
To measure house prices, the Real estate index for one- and two-dwelling buildings for permanent living is used (“Fastighetsprisindex”) in line with for example Claussen, 2013, Hort, 1998 and Leonhard et. al., 2013. This quarterly Index is available from Sta- tistics Sweden on the regional level9.
A drawback measuring real house price development in this way is that it does not con- tain information about tenant-owned apartments or apartments in co-operative build- ings. Unfortunately, inclusion of such data is not possible for the sample period. Yearly data on tenant-owned properties is only available from 2000 and onwards. The decrease in the sample size it would mean to include them in the already quite short time series argues against it. The Real estate index for one-and two-dwelling buildings for perma-
8 For example, the Swedish financial crisis in the beginning of the 90s and the structural break when Sweden went from a currency peg to a floating exchange rate is avoided.
9 The region used is Stockholm county.
Figure 1: Real house prices (In logs), 1996q1-‐‑2015q4.
nent living is therefore the best available measure. The index measures prices on actual sales, a few months before the actual registration date. Therefore, it seems appropriate to follow Claussen (2013) and interpret the price index for quarter 𝑡 as measuring the price at quarter 𝑡 − 1. The index will be deflated using the consumer price index with constant taxes (CPIF).
User costs of owning a dwelling is measured using the real mortgage rate, since this was the single factor affecting the user cost of owning a dwelling the most as discussed in section two. Therefore, it will be measured in the following way:
𝑅; = 𝑟; 1 − 𝜏; − 𝜋;, (4)
where 𝑟; is the mortgage rate and 𝜏; the tax-deductible part of the mortgage rate10. The after tax mortgage rate is deflated by CPIF, represented by 𝜋;. The mortgage rate is approximated by weights of the floating11, long term12 fixed and short term13 fixed mortgage rate available from three of the largest Swedish Banks, Nordea, SEB and Swedbank14. The weights are calculated using the share of borrowing from Swedish mortgage institutes to the households consisting of long term, short term and floating mortgage rates15 allowing for time variation in the combination of the different rates.
Since the fraction of mortgages with different terms has changed over the sample period this seem important to include. During more recent years the share choosing a floating interest rate have increased (Boverket, 2008; Holmberg et al, 2015; Söderström et al, 2013).
The mortgage rates available from the banks are the so-called “listed rates”. The “true”
mortgage rate would probably be most accurately measured using the average interest rate offered by the banks in Sweden. However, such data is not available for then sam- ple period. It was not until June 1st 2015 that the Swedish Supervisory Authority im- plemented a new law stating that banks now should provide information on the average mortgage rate given to its costumers (FSA, 2015b). Even though the listed rates are not actual rates paid by customers following negotiation with the mortgage originators, it is
10 After the tax reform 1991, the tax deductible rate for Swedish mortgages have been 30 percent (Boverket, 2008).
11 Fixed less then one year.
12 Fixed more then five years.
13 Fixed more than one but less then five years.
14 There were unfortunately no data available over the sample period from SHB also one of the big Swedish banks.
15 The weights were provided by Eric Spector at the Riksbank whom I would like to thank for assisting me with this.
the best available approximation since the spread between the mortgage rates and for example the repo rate has increased during recent years (Leonhard et al, 2013). The data is unavailable on the country level and assumed to be the same in Stockholm County as in Sweden. This is not an unreasonable assumption, but the true mortgage rate could be slightly lower for Stockholm, since the discounts on the mortgage rate for high-income takers could be larger.
To measure income, seasonally adjusted16, real disposable income less taxes in millions per capita, available from Statistics Sweden’s financial accounts, is used. The variable is not available on the regional level but will work as an approximation even though in- come is likely higher in a metropolitan area compared with the entire nation.
Statistics Sweden supplies a measure of total financial assets held by households. This will be used to measure Financial Wealth. Financial assets include bonds, shares and equity as well as funds, insurances and currency held at bank accounts. This measure is available quarterly on the country level from 1996 and onwards. The series is deflated using CPIF and taken per capita.
Population has little variation and in most cases a very steady upward trend. Therefore, the variable probably contains to little variation for co-integration to be recognized.
Since it is not possible to locate data on the regional level with an age distribution it was not possible to take the approach by for example Caldera et al (2011) or Hort (1998) were the population aged between 25-44 years are used as population measure17. The approach will instead be to take the change of the size of the population containing all age groups. Statistics Sweden has unfortunately no historical quarterly data saved on population. From 2004 monthly data is obtain from Stockholm Municipality18 . It is transformed into quarterly data taking a weighted average. To obtain a full series it is truncated with yearly data approximated to quarterly data using a cubic spline19 in line with Turk (2015). To capture the effects of a housing shortage, population change will be taken in relation to the amount of new dwelling. This variable will be referred to as the demographics variable. Data on dwellings in newly constructed buildings are avail-
16 The seasonal adjustment was done in Eviews, using the U.S. Census Bureau’s X-13 seasonal adjustment tool.
17 The advantage of this approach is that the demand for housing is argued to be particular high in this age group.
18 I would like to thank Frida Saarinen at Sweco for providing me with this data.
19 This was done in excel, using the qubic spline function SRS1 Cubic Spline.
able quarterly and on the regional level through statistics Sweden. The series was sea- sonally adjusted before construction of the demographics variable.
Construction costs is approximated using the quarterly Factor price index for buildings deflated by CPIF. Unfortunately, it is not available on the county level. Therefore, this measure approximates the county level even though there is reason to believe that con- struction costs could be higher in Stockholm compared to the whole country. Also, it does not include information on land prices, which could matter for the supply of hous- ing in Stockholm. Nevertheless, construction costs seem too important for house prices to leave out. The time series of the included variables except from the real house prices are presented in figure 2 below. Next, the the empirical results are presented.
Figure 2: Time series over other variables included, 1996q1-‐‑2015q4.
6. Results and discussion 6.1 Unit root testing
The first step is to investigate if the variables are stationary. As mentioned earlier, the variables should be non-stationary in levels and stationary in their first order difference for a potentially co-integrating relationship to exist. The tests used are the Augmented
Dicker Fuller Test20 (ADF-test) and the Kwiatkowski-Phillips-Schmidt-Shin21 test (KPSS- test) for unit roots. The expected results are that real house prices, real disposa- ble household income, construction cost and real financial assets are increasing and non-stationary in levels and stationary in their first order difference. Figures 2 strength- ens this hypothesis. The real mortgage rate however, should be stationary in the very long run according to theory. Results from previous studies show that in shorter hori- zons, the real mortgage rate could be non-stationary (Beechey et al, 2008; Claussen 2013). The demographics variable is also less clear and the graph does not give a clear answer. The variable on population in Stockholm does look increasing and could be non-stationary in levels.
The results from the tests can be found in table 4 in Appendix. First, the tests are ap- plied on the level specifications of the variables. Thereafter the tests are performed again, on their first difference. The lags included are chosen using the Akaike infor- mation criterion22. The ADF and KPSS-test confirms that real house price, real financial wealth and real construction costs are stationary in their first difference. The income variable is I(1) according to the ADF-test, but non-stationarity is just rejected on the 5 percent level by the KPSS-test. Relying on theory and the result from the ADF-test, real income is assumed to be I(1). The result in all tests on the real mortgage rate suggests it to be I(1), at the horizon of this sample. Moving on to the the demographics variable, both the ADF-test and KPSS-test suggests it to be I(1). Summing up, the conclusion from the unit-root testing is that all the variables are I(1). The next step will be to inves- tigate if there exist co-integration between the variables.
6.2 Results from the Johansen Procedure
There are several procedures to test co-integration. In this study the Johansen procedure and the Engle-Granger are considered, as discussed earlier. Johansen derived two tests for co-integration, the Trace statistic23 and Maximum Eigenvalue statistic24. The test procedure of both tests is sequential. First, one test the null hypothesis of no co-
20 More technical information on the ADF-test can be found in Wooldrich (2010).
21 More technical information on the KPSS-test can be found in Wooldrich (2010).
22 AIC makes a trade off between the fit and the number of included parameters in the following way: 𝐴𝐼𝐶 = ln ||} Qt + 𝑝 + 1 tC.
23 𝜆;•€•‚ 𝑟 = −𝑇 ln 1 − 𝜆I 𝑛I= 𝑟 + 1, Where 𝜆I are the estimated values of the characteristic roots and 𝑇 is the number of usable observations.
24 𝜆ƒ€„𝑟, 𝑟 + 1 = −𝑇 ln 1 − 𝜆•dB .
integration, 𝐻p, against the alternative of at least one co-integrating vector, 𝐻…. Reject- ing 𝐻p, in the initial stage, one continues testing the hypothesis, that there exist only one co-integrating vector against the alternative of at least two and so on. The procedure is repeated until the null hypothesis is accepted. The results from the test are shown in table 5 in appendix.
A large number of models are tested. The lags included in each model was selected us- ing the procedure suggested by Enders (2010), where a vector auto-regression (VAR) is estimated using the un-differenced data and use same lag length test as in a traditional VAR. For Model A, containing real house prices, real household income and the real, the trace test finds one co-integrated vector, but the lambda max test indicates none.
Lütkepohl et al. (2001) have concluded that empirically, the power of the trace test is higher than that of the maximum eigenvalue test. Therefore, it is assumed to exist one co-integrating vector. Model B, containing real house prices, financial wealth and the real mortgage rate have one co-integrating vector according to both tests. With Model C, real income is added to specification B, and Model D, where the demographics vari- able is added to model specification B, the same scenario as in model A occurs. Here, one co-integrating vector is also assumed for the same reasons. In model E, construction costs are added to model specification B. The trace test indicates two co-integrating vectors on the five percent significance level, but on the one percent level one co- integrating vector. The max test on the other hand indicates one co-integrating vector on the five percent level. Looking at the result found in previous studies towards one co- integrating relationship, this seems more reasonable. Also, the test indicates one co- integrating vector for all the other specifications. The tests were also conducted on a model including all variables. Here one co-integrating vector is found. The conclusion is therefore that for all models in table two, one co-integration relation exists.
Concluding that there exist a long-run relationship between the variables, the specifics of this relationship will now be investigated. Table three presents the long run and error correction parameters of the models presented above. The long run parameters (the co- efficients of the beta vector) is interpreted as elasticities, in line with the previous stud- ies presented in section three.
In table six in Appendix, a brief summary of the findings of previous studies are pre- sented. It is important to note that the different studies use different methods, numbers of explanatory variables and somewhat different definitions of the variables and there- fore the numbers are not directly comparable but they still provide important infor- mation that can be used fore comparison of results. The result from the long run rela- tionship as well as the error correction parameters is presented below in table 1.
Table 1: Long run & error correction parameters from the Johansen procedure
Model A Model B Model C Model D Model E
𝛽 𝛼 𝛽 𝛼 𝛽 𝛼 𝛽 𝛼 𝛽 𝛼
ℎ𝑝𝑖 1.00 0.01 1.00 -‐‑0.15 1.00 -‐‑0.14 1.00 -‐‑0.11 1.00 -‐‑0.17
NA (0.72) NA (-‐‑4.01) NA (-‐‑3.94) NA (-‐‑2.17) NA (-‐‑4.44)
𝑖 -‐‑1.79 0.07
-‐‑0.11 0.004
(-‐‑6.22) (3.86)
(-‐‑0.94) (0.06)
𝑓
-‐‑0.80 -‐‑0.17 -‐‑0.75 -‐‑0.18 -‐‑0.81 -‐‑0.19 -‐‑0.58 -‐‑0.25 (-‐‑30.31) (-‐‑2.36) (-‐‑13.99) (-‐‑2.49) (-‐‑29.48) (-‐‑1.86) (-‐‑4.95) (-‐‑3.48)
𝑟 0.16 -‐‑1.04 0.06 -‐‑6.06 0.06 -‐‑6.22 0.05 -‐‑6.26 0.04 -‐‑5.11
(3.61) (-‐‑2.88) (5.75) (-‐‑5.93) (5.99) (-‐‑6.05) (4.71) (-‐‑4.33) (4.48) (-‐‑4.30) 𝑑𝑒𝑚
0.02 -‐‑1.25
(1.47) (-‐‑0.68)
𝑐𝑐
-‐‑0.79 -‐‑0.05
(-‐‑2.00) (-‐‑2.53)
𝑐𝑜𝑛𝑠 21.28 NA 7.13 NA 8.09 NA 7.20 NA 6.46 NA
(5.84)
(25.03)
(7.52)
(24.38)
(14.73)
Tests 𝑋C p-‐‑value 𝑋C p-‐‑value 𝑋C p-‐‑value 𝑋C p-‐‑value 𝑋C p-‐‑value
Arch* 197.12 0.18 190.66 0.28 518.19 0.28 500.33 0.49 514.75 0.31
JB* 9.96 0.13 4.64 0.59 10.86 0.21 10.85 0.21 10.08 0.26
PT* 94.07 0.01 121.43 0.67 130.54 0.17 128.56 0.03 254.60 0.11
BG*1 5.91 0.75 4.86 0.85 10.81 0.82 22.88 0.13 21.32 0.16
BG 2 12.75 0.81 13.58 0.76 23.08 0.88 41.19 0.13 36.32 0.27
BG 4 39.72 0.31 40.10 0.29 78.01 0.11 99.96 0.002 100.62 0.002
*T-‐‑valuses in brackets ()
*Arch test the null of no arch in the residuals.
*JB= Jarque Bera tests the null of normally distributed residuals.
*PT= portmanteau test examines the null hypothesis of independence in residuals.
*BG =Breusch-‐‑Godfrey test for the null of non serially correlated errors.
lags 1, 2 and 4 are used in line with Barot & Yang (2002).
Note: Adding more lags did not help remove the remaining autocorrelation from model 1, 4 and 5. The ordering of the varia-‐‑
bles could influence the PT and LM-‐‑test. All estimations also include seasonal dummies which are not shown due to space.
hpi=Real house prices, i=real income, r= real mortgage rate, f= real financial wealth, cc=construction costs, dem=demographics.
Theoretically, the income elasticity should be higher than one; increasing income leads to a larger increase in spending on housing. In model A, the income elasticity is signifi-
cant at 1.79 suggesting that increasing income with one percent leads to an increased long run house price with 1.79 percent. The coefficient is somewhat larger than that found in for example Claussen (2013) of 0.8-1.4, and Turk (2015) of 1.3. However, it is smaller than 2.82 found by Caldera Sánches & Johannson (2001). The semi-elasticity of the real mortgage rate is substantially larger than that of previous studies. In model A, a one percent decrease of the real mortgage rate would lead to an increase of the long run equilibrium house prices of 16 percent. There is still some autocorrelation left in the residuals, but it passes all other diagnostics.
In model B the coefficient on the real mortgage rate is 0.06; a one percent increase in the real mortgage rate would lead to a lowering of the long run equilibrium house price by 6 percent. This number is exactly that found by Claussen (2013). Increased financial wealth of one percent mean an increase of house prices by 0.8 percent. This elasticity is larger than findings of previous studies. One explanation could be that they focus on Sweden and not Stockholm. The average house prices in Stockholm was more than twice as high in an absolute sense the last quarter of 2015 compared to the country as a whole25, making the capital requirement is much larger in an absolute sense. Therefore, it seems reasonable that financial wealth has a larger impact in Stockholm compared to Sweden as a whole. The model shows significant error correction from house prices;
deviations between the short run and long run equilibrium level of real house prices is closed on average by 15 percent per quarter. The number is in line with most previous studies, where the results range between 4-15 percent. The exception is Hort (1998) who found a yearly error correction of 84 percent. Translating the 15 percent correction from quarterly to yearly terms means a closing of the gap by 48 percent26 on average on a yearly basis, which is about half of that found by Hort. Model B pass all the diagnos- tic tests.
In model C, real income is added to specification B. Here, income turns insignificant but the parameters on financial wealth and the interest rate do not change much. The error correction shifts slightly downwards to 0.14. The model passes all diagnostics tests.
25 The average purchase price one- and two-dwelling buildings for permanent living in Sweden was 2 550 000 SEK compared to 5
383 000 SEK in Stockholm county the last quarter of 2015 (SCB, 2016).
26 According to the formula: 1 − 0.15¯≈ 0.522 and 1 − 0.522 ≈ 0.48.
With specification D, the demographics variable is added to specification B. The de- mographics variable enters insignificantly with the wrong sign. Also here, financial wealth and the interest rate do not change much from B. The error correction parameter on house prices changes from- 0.15 to -0.12. This model does not pass the BG-test for autocorrelation on the fourth lag.
In model E, construction costs are added to specification B. A one percentage increase of real financial wealth would lead to an increase of the long run equilibrium house price level with 0.58 percent. This is slightly lower compared to that found in specifica- tion B. The effect of changes in the interest rate also slightly dampens under this speci- fication. Instead of a 6 percent adjustment of the long run equilibrium house price to a 1 percent change of the real mortgage rate, it drops to 4 percent. A one percent increase of construction costs would lead to an increase of the long run house price level of 0.79 percent. This is not that much different from the increase of 0.6 percent found by Adam and Füss (2010). The error correction parameter increases from 15 to 17 percent and the yearly gap is closed by 53 percent.
None of the presented models contain all variables. Including all variables generates strange results in the way that the coefficients comes out with the wrong size and sign according to theory and previous studies. Therefore, the larger models were found unre- liable and left out. The same goes for models including income in combination with construction costs or demographics. No such model worked well in the sense that the outcomes were strange. In models including both income and construction costs, either the income variable comes out with the wrong sign and the construction costs variable is blown up, or the other way around. Claussen (2013) had similar results leading to the exclusion of construction costs.
Except for the error correction parameter, the estimations of the short run dynamics can be hard to interpret (Claussen, 2013). But what can be said, from table eight in appen- dix, is that the results indicate persistence in house price with positive significant coef- ficients on lagged house prices. The real mortgage rate and financial wealth both seem to have a contemporaneously effects on house prices with coefficients ranging. In mod- els C income also seem to influence house prices contemporaneously.
The conclusion is that increased real income, financial wealth and construction costs in combination with lowering of the interest rate can help explain the rise in real house prices both in the long and the short run. Next, the dynamics of house prices will be further investigated using impulse response functions and forecast error variance de- compositions.
6.3 Impulse responses and Forecast Error variance decompositions
Using the VECMs it is possible to compute Impulse Response Functions (IRF) and Forecast Error Variance Decompositions (FEVD)27. IRFs are used to investigate the dynamic interactions between the endogenous variables. There are several methods acknowledged in the literature to identify the shocks. Here, orthogonal IRFs will be used following the arguments by Plaff (2008) since they are suitable if the underlying shocks are less likely to occur in isolation, but contemporaneous correlations between the components of the error process could exist. The orthogonal impulse responses are derived from a Choleski decomposition of the error variance-covariance matrix. The matrix is lower triangular meaning that only a shock in the first variable of the system will exert influence on the remaining ones in the first period. The second and following variables will not have a direct impact on the first variable in the system, but will in- stead have an impact with a lag. This means that the ordering of the variables could matter for the outcome. However, the Choleski decomposition allows for identification using the minimum number of assumptions needed. The ordering of the variables are set to [ hpi, i, f, r, dem, cc ]28. The motivation for this specific ordering, since short run restrictions are the ones imposed here, is that the ones believed to have the most immediate impact on house prices are set prior to the others. To put the de-‐‑
mographics variable and real construction costs at the end therefore is reasonable since they are quite rigid in the short run.
The IRFs generated from the different models are presented in figure 3-7. The interpre- tation of the IRFs should be such that they are responses to a standard deviation shock in the impulse variable. To be able to understand the magnitudes of the effects the standard deviations on all the variables in all the models can be found in table seven in Appendix.
27 For more technical information on IRFs and FEVDs, see Enders 2010 or Plaff, 2008.
28 Thus, the ordering under the different specifications are: A [hpi, i, r], B [hpi, f, r], C [hpi, i, f, r], D [hpi, f, r, dem], E [hpi, f, r, cc].
All models show significant persistence in house prices at the two-year horizon, thereaf- ter it turns insignificant except under specification A. The impulse responses from real income and the real mortgage rate is insignificant in A. In model B house prices show significant responses to shocks in both real financial wealth and the real mortgage rate.
A positive shock to real financial wealth of one standard deviation results in a signifi- cant increase in house prices. The maximum effect is reached within the first three years and are persistent at the same level thereafter, at almost 4.5 percent. A one standard deviation positive shock to the real mortgage rate results in lower house prices and the maximum effect of 4 percent also is reached at the three-year horizon.
Figure 3: Orthogonal Impulse responses from HPI, model A. Figure 4: Orthogonal Impulse responses from HPI, model B.
Figure 5: Orthogonal Impulse responses from HPI, model C. Figure 6 Orthogonal Impulse responses from HPI, model D.
Figure 7: Orthogonal Impulse responses from HPI, model E.
In model C, a standard deviation shock to real disposable income shows a small signifi- cant effect at the first year horizon, but then turns insignificant for the future periods.
The response of house prices to shocks in the real mortgage rate and real financial wealth are similar to those in model B, but since the size of the shocks differ, one stand- ard deviation is not the same for the models, the effect from real income is larger in model C while the effect from the interest rate is smaller. In model D the maximum response to shocks in the mortgage rate and financial wealth are reached about one year later compared to model B and C, and the effect from the mortgage rate is close to the
rejection level of 5 percent level for almost all periods. The maximum effects are the same as from model C since the standard deviations are the same, and the responses are alike. There is no significant response from house prices from a shock in the de- mographics variable. Under specification E, real financial wealth and the real mortgage rate once again show similar results to those of model C and D. Shocks to construction costs also have a significant and positive effect on real house prices. The maximum ef- fect is reached at the four-year horizon where a shock to real construction costs of seven percent result in a permanent increase in house prices by two percent. Since the ordering of the variables could matter for the outcome, IRFs using different orderings have ben computed. However, these results show no important differences. For the case of brevi- ty, these results are left out.
FEVDs makes it possible to examine proportion of different innovations in the variables that contribute to the volatility in house prices. These give indications on the main fac- tors driving house prices at different horizons. The results come out as a percentage figure. The FEVDs are based on the orthogonalized IRFs, making them sensitive to the same problems with the ordering of the variables. The effects of the assumptions should however be reduced at longer horizons since the variance decompositions should con- verge with 𝑛 (Enders, 2010). Table 2 show the results from the FEVDs. Under specifi- cation A, all variation in house prices is explained by its own volatility.
Model B give a different picture. House prices only account for 72 percent of its volatil- ity at the first year horizon. Real financial wealth explains close to 20 percent and the real mortgage almost 10 percent. Already at the third year horizon, financial wealth ex- plains close to 50 percent of the changes in real house prices, 20 percent is due to real mortgage rate shocks and only 30 percent to own volatility. Thereafter the effects do not change much. Similar results can be found under specification C and D. Under C real income show a persistent effect of around 5 percent at all horizons. In model D de- mographics is exogenous and does not seem to affect house price movements, at any horizon. In model E similar effects are found from financial wealth and the mortgage rate as model B, C and D, but the contribution of own volatility in house prices drops more compared to the other models. Construction costs accounts for a persistent effect of 10 percent from the second year horizon and onwards.
